Gravitation quiz

The SI unit of G is:

If the distance between two masses is doubled, the gravitational force becomes:

Kepler's second law is also called the law of:

The escape speed of a body from the Earth:

For planets, T^2 is proportional to:

As we go up from the Earth's surface, g:

The total energy of a satellite in a circular orbit is:

A planet with the same density as the Earth but twice its radius has acceleration due to gravity:

The escape speed from the Earth is about:

The force on a mass placed inside a uniform spherical shell is:

State Kepler's law of orbits and law of periods. (2 marks)

State Newton's universal law of gravitation. (2 marks)

Why is g at the poles greater than at the equator? (2 marks)

Find g at a height of 32 km above the Earth's surface. (2 marks)

Show that Kepler's second law follows from the conservation of angular momentum. (2 marks)

Define gravitational potential energy and write its expression at distance r from the Earth's centre. (2 marks)

Find the orbital speed of a satellite just above the Earth's surface. (2 marks)

Why does the Moon have no atmosphere? (2 marks)

How does the period of a satellite change if its orbit radius becomes four times larger? (2 marks)

Write the expressions for the kinetic, potential and total energy of a satellite in a circular orbit. (2 marks)

Find the period of a satellite orbiting just above the Earth's surface. (3 marks)

Find the gravitational potential energy of a 100 kg body on the Earth's surface. (3 marks)

The Moon has g = 1.62 m/s^2 and radius 1.74 x 10^6 m. Find its escape speed. (3 marks)

Find the gravitational force between two lead spheres of 10 kg and 20 kg whose centres are 0.5 m apart. (3 marks)

At what depth below the surface will g be 25% less than at the surface? (3 marks)

Read the passage and answer the questions. The International Space Station orbits about 400 km above the Earth. Take GM = 4.0 x 10^14 N m^2 kg^-1 and R = 6.4 x 10^6 m. (i) Find the radius of its orbit. (ii) Find its orbital speed. (iii) Find its period in minutes. (5 marks)

Read the passage and answer the questions. An astronaut stands on the Moon, where g = 1.62 m/s^2. Her mass is 60 kg. (i) Find her weight on the Moon. (ii) Find her weight on the Earth. (iii) Does her mass change? Explain. (5 marks)

Read the passage and answer the questions. The Earth's distance from the Sun is 1.47 x 10^11 m at perihelion and 1.52 x 10^11 m at aphelion. (i) Where is the Earth fastest? (ii) Find the ratio of its speeds at perihelion and aphelion. (iii) Name the law used. (5 marks)

Read the passage and answer the questions. A scientist compares two planets of equal mass. Planet X has radius R and planet Y has radius 2R. (i) Compare g on the two planets. (ii) Compare their escape speeds. (iii) From which planet is it easier for a rocket to escape? (5 marks)

Read the passage and answer the questions. A satellite of mass m orbits the Earth at radius r. (i) Write the gravitational force on it. (ii) Equate it to the centripetal force and find the orbital speed. (iii) Show that its kinetic energy is half the magnitude of its potential energy. (5 marks)

State Kepler's three laws of planetary motion. Explain how Newton's law of gravitation explains the third law for circular orbits. (6 marks)

Derive the expression for the acceleration due to gravity at a depth d below the Earth's surface. Compare it with the variation of g with height. (6 marks)

Derive the expression for gravitational potential energy of a mass m at distance r from the Earth's centre. (6 marks)

Derive the orbital speed, period and total energy of a satellite in a circular orbit around the Earth. (6 marks)

Explain the shell theorem and its use in finding the gravitational force inside and outside the Earth. (6 marks)